- #1

mathsnerd2

- 3

- 0

DecisionProblemsinGroupTheory(L24).... ....5

LieAlgebrasandRepresentationTheory(M24)... ...5

ModularRepresentationsofFiniteGroups(L24)... ...6

Calculusandalgebra(L24)...... ...8

Representationsof?nitegroupsofLietype(L24)... ....8

CommutativeAlgebra(M24)...... ...9

Non-commutativealgebras(L24)...... ...9

VonNeumannAlgebras(L24)...... ...10

Analysis 12

TopologicalGroups(L24)....... ...12

TopicsinIn?niteGroups(M16)..... ...12

AnalysisontheDiscreteHypercube(L24)— Non–Examinable ....13

IntroductiontoFunctionalAnalysis(M24)..... ...14

ComplexDi?erentialEquations(L24)...... ....15

Ellipticpartialdi?erentialequations(M24)... .....15

Combinatorics 17

Combinatorics(M16)....... ...17

CombinatorialProbability(L16)...... ....17

HypergraphGames(E8)— Non–Examinable ......18

ArithmeticCombinatorics(M16)...... ...18

GeometryandTopology 19

TheX-raytransformingeometryanddynamics(L24)... ...19

AlgebraicTopology(M24)....... ...20

Di?erentialGeometry(M24)...... ...20

SpectralGeometry(L24)........ ...21

AlgebraicGeometry(M24)....... ...22

ComplexManifolds(L24)........ ...22

AlgebraicGroups(M24)...... ...24

FibreBundles(L16)........ ...24

AlgebraicCycles(L24)...... ...25

Logic 26

CategoryTheory(M24)...... ...26

SetTheoryandLogic(L24)....... ...27

NumberTheory 29

EllipticCurves(L24)...... ...29

LocalFields(M16)....... ...29

ErgodicTheory(L24)....... ...30

TheIwasawatheoryofellipticcurveswithcomplexmultiplication(L24)....31

AlgebraicNumberTheory(M16)..... ...31

ModularFormsandAutomorphicForms(L24)... ...32

Non-abelianLubin-Tatetheory(M24)— Non–Examinable ......32

Probability 3

AdvancedProbability(M24)...... ...3

StochasticNetworks(L24)...... ...3

StochasticLoewnerEvolutions(L16)...... .....3

StochasticCalculusandApplications(L24).... ...3

ParticlePhysics,QuantumFieldsandStrings 46

QuantumFieldTheory(M24)...... ...46

SymmetryandParticlePhysics(M24)...... ...47

StatisticalFieldTheoryandApplications(M24)... ....48

AdvancedQuantumFieldTheory(L24)...... ...49

StringTheory(L24)........ ...49

SupersymmetryandExtraDimensions(L24)... ....50

StandardModel(L24)....... ...51

SolitonsandInstantons(E16)..... ...52

Supergravity(E16)........ ...53

3

QuantumInformationandQuantumFoundations 54

IntroductiontoQuantumComputation(M16)..... ....54

QuantumInformation,EntanglementandNonlocality(M16). .....55

PhilosophyofClassicalandQuantumMechanics(M12,L12).. ....55

MathematicalAspectsofQuantumInformationTheory(L24). .....56

QuantumControl(L16)...... ...57

RelativityandGravitation 59

Cosmology(M24)........ ...59

GeneralRelativity(M24)....... ...61

AdvancedCosmology(L16)....... ...62

ApplicationsofDi?erentialGeometrytoPhysics(L24)... ......63

BlackHoles(L24)....... ...64

QuantumCosmology(E16)........ ...65

IntroductionToTwistorTheory(E16)...... ...66

Astrophysics 67

AstrophysicalFluidDynamics(M24)...... ....67

StructureandEvolutionofStars(M24)..... ....68

AccretionDiscs(L16)...... ...68

Galaxies(L24)......... ...69

PhysicalCosmology(L24)....... ...70

StellarandPlanetaryMagneticFields(L24).... ...71

I am interested in differential geometry, group theory, a bit of quantum mechanic, some algebra, complex analysis and topology.

So right now I can't decide what area I want to major in? How do you guys decide what area to specialize?

What subject I should choose so that I can still keep in touch with my favorite topics (differential geometry, group theory, a bit of quantum mechanic, some algebra, complex analysis and topology) ?

Please help me I am clueless.

I only allowed to take 10 course from the list above and hopefully the course that I choose will be useful in my research for PhD ( still haven't decide what topic).

Thank you for your help. :)